MinT - Best Known (29, 29+37, s)-Nets in Base 81

Best Known (29, 29+37, s)-Nets in Base 81

(29, 29+37, 370)-Net over F₈₁ — Constructive and digital

Digital (29, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(29, 29+37, 581)-Net over F₈₁ — Digital

Digital (29, 66, 581)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(29, 29+37, 735845)-Net in Base 81 — Upper bound on s

There is no (29, 66, 735846)-net in base 81, because

1 times m-reduction [i] would yield (29, 65, 735846)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11259 944167 614570 048866 614467 855075 070418 115260 121782 383384 284501 712837 204326 024369 760845 010800 081420 137911 677736 739398 005441 > 81⁶⁵ [i]